Higher amalgamation in $\mathrm{ACFA}^{+}$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918278254821376 |
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| author | Ludwig, Stefan Marian |
| author_facet | Ludwig, Stefan Marian |
| contents | We show two results on higher amalgamation in the theory $\mathrm{ACFA}^{+}$, the model companion of the theory of difference fields with an additive character (added as a continuous logic predicate) on the fixed field in characteristic 0. On one hand, we show that the non-trivial condition for 3-amalgamation established in a preceding paper is not sufficient for 4-amalgamation. On the other hand, we show that when working over substructures whose $\mathcal{L}_σ$-reduct is a model of $\mathrm{ACFA}$, $n$-amalgamation holds for all $n\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05096 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher amalgamation in $\mathrm{ACFA}^{+}$ Ludwig, Stefan Marian Logic Primary 03C60, Secondary 03C66, 12L12, 03C45 We show two results on higher amalgamation in the theory $\mathrm{ACFA}^{+}$, the model companion of the theory of difference fields with an additive character (added as a continuous logic predicate) on the fixed field in characteristic 0. On one hand, we show that the non-trivial condition for 3-amalgamation established in a preceding paper is not sufficient for 4-amalgamation. On the other hand, we show that when working over substructures whose $\mathcal{L}_σ$-reduct is a model of $\mathrm{ACFA}$, $n$-amalgamation holds for all $n\geq 3$. |
| title | Higher amalgamation in $\mathrm{ACFA}^{+}$ |
| topic | Logic Primary 03C60, Secondary 03C66, 12L12, 03C45 |
| url | https://arxiv.org/abs/2601.05096 |